Microclimate libraries

Table of Contents

• Meteorological variables
  • Radiation
• Incoming longwave radiation

Meteorological variables

Radiation

• Stefan–Boltzmann equation for the power radiated from a black body in terms of its absolute temperature \( T\):

  \[ P = \sigma \cdot T^4 \]

• Global radiation depending on latitude ...
• Mean temperature \( \overline{T} \) after Thornton [thornton:1997a:]

  \[ \overline{T} = 0.394 \cdot T_{min} + 0.606 \cdot T_{max} \]

Sun declination

Eccentricity factor for calculation of extraterrestrial radiation ([fortin:2008a])

Daily extraterrestrial radiation as developed by [sellers:1961a] (cit. in [fortin:2008a], and [cai:2007a]) note: formula of sun declination wrong in [fortin:2008a]

Ratio between diffuse and total solar irradiance after [friend:2001a]

[lizaso:2005a]

Daylength

Daylength period

The daylength is calculated based on latitude and the day of the year according to [lee:2010a], as:

\[ dayl = 12.0 * \frac{PI + 2.0 * arcsin( sinld_cosld ) }{PI} \]

with:

\[ sinld_cosld = \frac{ -sin( \frac{-PI}{45.0} ) + ( sin( lat_r) * sin( sdec) ) } { cos( lat_r) * cos( sdec) } \]

With sdec beeing sun declination and lat_r latitude in radians:

\[ sdec = 0.4093 * sin( \frac{ 2.0 * PI * jday }{ 365.0 - 1.405 } lat_r = lat * \frac{ PI }{ 180.0 } \]

Saturated vapor pressure according to [hamon:1963a]

When foliage temperature is above 0oC, saturated vapor pressure is calculated as:

\[ svp = 0.61078 * \exp(17.26939 * \frac{T}{T + 237.3}) \]

When foliage temperature is below 0oC, it is:

\[ svp = 0.61078 * \exp(21.87456 * \frac{T}{T + 265.5}) \]

Annual mean temperature

Incoming longwave radiation

Incoming longwave radiation is given by:

\[ LWR_{in} = \varepsilon \sigma T^4 \; , \]

wherein \( \varepsilon, \sigma, T \) refer to the emissivity, the Stefan-Boltzmann constant and air temperature, respectively.

The emissivity \( \varepsilon \) has two components , i.e., emissivity under clear ( \( \varepsilon_{cl} \)) and clouded sky ( \( \varepsilon_{cl} \)):

\[ \varepsilon = (1 - f_{cl}) \varepsilon_{cs} + f_{cl} \varepsilon_{cl} \]

The partitioning coefficient \( f_{cl} \) refers to the cloud fracion. For \( \varepsilon_{cl} \), a constant value of 0.976 is used [greuell:1997a].

Clear sky atmospheric emissivity
Emissivity of incoming longwave radiation under clear sky conditions is calculated based on vapour pressure \( vp \) [brunt:1932a] :

\[ \varepsilon_{cs} = B_c + B_d \sqrt{vp} \]

The parameters \( B_c \) and \( B_d \) are set to 0.53 and 0.212, respectively [kraalingen:1997a].

Cloudiness
Cloudiness is derived from global radiation using the Angstrom formula:

\[ f_{cl} = \frac{\frac{SWR}{SWR^{\ast}} - A}{B} \]

using the Angstrom parameters \( A = 0.29 \) and \( B = 0.52 \) [kraalingen:1997a].